GCF of 774/180, 729/595
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 774/180, 729/595 i.e 9/21420 easily. The following is the detailed procedure to determine the greatest common factor of fractions 774/180, 729/595.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 774/180,729/595?
Given fractions are 774/180,729/595
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 774/180,729/595, numerators are 774,729
Denominators are 180,595
The GCF of 774,729 is 9 .
LCM of 180,595 is 21420.
The greatest common factor of 774/180,729/595 = [GCF of 774,729]/[LCM of 180,595]= 9/21420
Therefore, the GCF of 774/180,729/595 is 9/21420.
To find the highest common factor of 774,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 774,729 is 9.
Lets's calculate GCF of 774,729
| 3 | 774, 729 |
| 3 | 258, 243 |
| 86, 81 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 774,729 By Matching Biggest Common Factor Method
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 774,729 . The biggest common factor number is the GCF number.
So the greatest common factor 774,729 is 9.
Lets's calculate LCM of 180,595
| 5 | 180, 595 |
| 36, 119 |
∴ So the LCM of the given numbers is 5 x 36 x 119 = 21420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/21420
Therefore, the GCF of Fractions 774/180,729/595 is 9/21420
Least Common Multiple of 180,595 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 180,595 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(180,595) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(180,595) x common factors =5 x 1 = 5
LCM(180,595) = ( 180 × 595 ) / 5
LCM(180,595) = 107100 / 5
LCM(180,595) = 21420
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FAQs on GCF of Fractions of 774/180, 729/595
1. What is the HCF of 774,729?
The HCF of 774,729 is 9
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 774/180, 729/595?
Answer: GCF of Numerators as per given numbers 774/180, 729/595 is
GCF of Numerators i.e. for 774,729 is 9
LCM of denominators i.e. for 180,595 is 21420.
Thus, GCF of Fractions is 9/21420.Finally, GCF of Fractions for 774/180, 729/595 is 9/21420.